{
  "Id": "fb89c80a-327e-4ddd-95f1-537d230efda5",
  "Title": "Playing with Numbers",
  "Subject": "Mathematics",
  "Topic": "Number Operations and Properties",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "Math-Ch02.pdf",
  "SessionMaterialId": "bf837b4c-03f6-4a6f-b091-a407c50c931a",
  "GeneratedAt": "2026-05-29T23:20:02.470537Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "The number 10 is a multiple of 5.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "Every multiple of 2 is an even number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "The HCF of co-prime numbers 9 and 14 is 3.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "Multiplying any number by 1 gives the same number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "The sum of two odd numbers is always odd.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "The number 1 is considered a prime number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "The smallest prime number is 2.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "Zero is neither positive nor negative.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "Multiplying two negative numbers gives a positive product.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "A prime number has exactly two distinct factors: 1 and the number itself.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "What is the first step in solving 14 \u002B 8 \u00D7 4 \u002B 194 \u00F7 7?",
      "Options": [
        "A. Addition",
        "B. Multiplication",
        "C. Division",
        "D. Subtraction"
      ],
      "Answer": "C. Division",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "Which operation should be performed first according to BODMAS?",
      "Options": [
        "A. Addition",
        "B. Multiplication",
        "C. Division",
        "D. Brackets"
      ],
      "Answer": "D. Brackets",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "What is the smallest prime number?",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 3",
        "D. 5"
      ],
      "Answer": "B. 2",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "The HCF of 4 and 15 is:",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 4",
        "D. None"
      ],
      "Answer": "A. 1",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "Which of the following numbers is divisible by 3?",
      "Options": [
        "A. 73",
        "B. 137",
        "C. 54",
        "D. 277"
      ],
      "Answer": "C. 54",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which number is a perfect number?",
      "Options": [
        "A. 496",
        "B. 459",
        "C. 495",
        "D. 469"
      ],
      "Answer": "A. 496",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "The 8th prime number minus the 12th prime number equals:",
      "Options": [
        "A. 30",
        "B. 14",
        "C. 18",
        "D. 28"
      ],
      "Answer": "B. 14",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "If a number is divisible by 90, it must be divisible by:",
      "Options": [
        "A. 7 and 45",
        "B. 9 and 11",
        "C. 8 and 18",
        "D. 5 and 9"
      ],
      "Answer": "C. 8 and 18",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Which digit should replace \u0027#\u0027 in 90##53 to make it divisible by 11?",
      "Options": [
        "A. 3",
        "B. 0",
        "C. 1",
        "D. 2"
      ],
      "Answer": "D. 2",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "What is the least number that can replace \u0027*\u0027 in 764*52 so it is divisible by 11?",
      "Options": [
        "A. 3",
        "B. 4",
        "C. 5",
        "D. 6"
      ],
      "Answer": "A. 3",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "The smallest prime number is _____.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "A number divisible by 10 ends with _____.",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "To solve 36 \u00F7 3 \u00D7 4, you should first perform the _____ operation.",
      "Options": [],
      "Answer": "division",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The LCM of 3 and 4 is _____.",
      "Options": [],
      "Answer": "12",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The HCF of two prime numbers always equals _____.",
      "Options": [],
      "Answer": "1",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "According to BODMAS, _____ should be solved first in the expression 4 \u002B (5 \u00D7 3).",
      "Options": [],
      "Answer": "brackets",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The sum of digits rule is used to check divisibility by _____.",
      "Options": [],
      "Answer": "3",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "The number _____ is both a factor of itself and 0.",
      "Options": [],
      "Answer": "1",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "Prime factorisation can be done using either the division method or the _____ method.",
      "Options": [],
      "Answer": "factor tree",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "A number divisible by both 5 and 9 is also divisible by _____.",
      "Options": [],
      "Answer": "45",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "If a number is divisible by both 6 and 8, what is the smallest such positive number? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 6 and 8\nStep 2: Prime factors of 6: 2, 3; Prime factors of 8: 2, 2, 2\nStep 3: LCM = 2\u00D72\u00D72\u00D73 = 24\nAnswer: 24",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "A car travels 150 km in 3 hours. What is its average speed? Show your working.",
      "Options": [],
      "Answer": "Step 1: Speed = Distance / Time\nStep 2: Speed = 150 / 3\nAnswer: 50 km/h",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "Find the least number of 5-digit divisible by 45. Show your working.",
      "Options": [],
      "Answer": "Step 1: 5-digit number: 10000\nStep 2: Prime factors of 45: 3\u00D73\u00D75\nStep 3: Least 5-digit = 45 \u00D7 223\nAnswer: 10035",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "A bus stops every 8th block and a tram stops at every 12th block. What is the first block they both stop at? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 8 and 12\nStep 2: Prime factors of 8: 2\u00D72\u00D72; Prime factors of 12: 2\u00D72\u00D73\nStep 3: LCM = 2\u00D72\u00D72\u00D73 = 24\nAnswer: 24",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "If three water tanks hold 5000L, 7500L, and 10000L respectively, what is the maximum container size to drain them exactly?",
      "Options": [],
      "Answer": "Step 1: Find HCF of 5000, 7500, 10000\nStep 2: Prime factors of 5000: 2\u00D72\u00D72\u00D75\u00D75\u00D75; Prime factors of 7500: 2\u00D73\u00D75\u00D75\u00D75; Prime factors of 10000: 2\u00D72\u00D72\u00D75\u00D75\u00D75\nStep 3: HCF = 5\u00D75\u00D75\nAnswer: 125",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "In a colony, there are 3 types of events every 4 days, 6 days, and 9 days. What is the first day they all coincide? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 4, 6, 9\nStep 2: Prime factors of 4: 2\u00D72; Prime factors of 6: 2\u00D73; Prime factors of 9: 3\u00D73\nStep 3: LCM = 2\u00D72\u00D73\u00D73 = 36\nAnswer: 36",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Calculate the number that should be added to 9813 to make it divisible by 5, 8, and 10.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 5, 8, 10\nStep 2: Prime factors of 5: 5; Prime factors of 8: 2\u00D72\u00D72; Prime factors of 10: 2\u00D75\nStep 3: LCM = 2\u00D72\u00D72\u00D75 = 40\nStep 4: Sum = 9813 \u002B x\nStep 5: Solve: 9813 \u002B x = multiple of 40\nAnswer: 27",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "If 764*52 needs to be divisible by 11, what single digit number replaces *? Show your working.",
      "Options": [],
      "Answer": "Step 1: Apply divisibility rule of 11: Sum of odd places - sum of even places\nStep 2: (7\u002B4\u002B5)-(6\u002B*\u002B2)\nStep 3: Solve =\u003E 16-(*\u002B8)=0 or multiple of 11\nAnswer: 3",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "Determine the smallest digit added to 31290876 to make it divisible by 5, 8, and 10. Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 5, 8, and 10\nStep 2: LCM = 40\nStep 3: Add digit x so that 31290876 \u002B x\nStep 4: Find smallest x such that 31290876 \u002B x = multiple of 40\nAnswer: 4",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "What number should be subtracted from 1002 to make it divisible by 3 and 4? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 3 and 4\nStep 2: Prime factors of 3: 3; Prime factors of 4: 2\u00D72\nStep 3: LCM = 2\u00D72\u00D73 = 12\nStep 4: Solve 1002 - x = multiple of 12\nAnswer: 2",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}